Uncertainty principle is one of the most amazing features of the mathematical foundation of quantum mechanics. The principle demonstrates the failure of simultaneous measurements of conjugate variables such as the position and momentum of a particle, which seems unexplainable in the realm of classical mechanics. In this talk we will discuss an analog of uncertainty principle in the field of symplectic and contact topology, namely the non-squeezing phenomenon which was discovered firstly by Gromov. By replacing wave functions by sheaves, We introduce a categorification procedure which plays the role of semi-classical "quantization" as it is done in quantum mechanics and extract a symplectic/contact invariant from the categorical operations. It turns out that this invariant becomes an obstruction of symplectic/contact squeezing phenomenon in a way similar to homological obstruction of homeomorphisms in basic algebraic topology.